diff --git a/src/backend/commands/vacuumlazy.c b/src/backend/commands/vacuumlazy.c
index 515ea9173d..a5c024cc19 100644
--- a/src/backend/commands/vacuumlazy.c
+++ b/src/backend/commands/vacuumlazy.c
@@ -349,6 +349,7 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 		Size		freespace;
 		bool		all_visible_according_to_vm = false;
 		bool		all_visible;
+		bool		has_dead_tuples;
 
 		/*
 		 * Skip pages that don't require vacuuming according to the visibility
@@ -500,6 +501,7 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 		 * requiring freezing.
 		 */
 		all_visible = true;
+		has_dead_tuples = false;
 		nfrozen = 0;
 		hastup = false;
 		prev_dead_count = vacrelstats->num_dead_tuples;
@@ -640,6 +642,7 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 				HeapTupleHeaderAdvanceLatestRemovedXid(tuple.t_data,
 											 &vacrelstats->latestRemovedXid);
 				tups_vacuumed += 1;
+				has_dead_tuples = true;
 			}
 			else
 			{
@@ -702,9 +705,22 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 			PageSetAllVisible(page);
 			SetBufferCommitInfoNeedsSave(buf);
 		}
-		else if (PageIsAllVisible(page) && !all_visible)
+		/*
+		 * It's possible for the value returned by GetOldestXmin() to move
+		 * backwards, so it's not wrong for us to see tuples that appear to
+		 * not be visible to everyone yet, while PD_ALL_VISIBLE is already
+		 * set. The real safe xmin value never moves backwards, but
+		 * GetOldestXmin() is conservative and sometimes returns a value
+		 * that's unnecessarily small, so if we see that contradiction it
+		 * just means that the tuples that we think are not visible to
+		 * everyone yet actually are, and the PD_ALL_VISIBLE flag is correct.
+		 *
+		 * There should never be dead tuples on a page with PD_ALL_VISIBLE
+		 * set, however.
+		 */
+		else if (PageIsAllVisible(page) && has_dead_tuples)
 		{
-			elog(WARNING, "PD_ALL_VISIBLE flag was incorrectly set in relation \"%s\" page %u",
+			elog(WARNING, "page containing dead tuples is marked as all-visible in relation \"%s\" page %u",
 				 relname, blkno);
 			PageClearAllVisible(page);
 			SetBufferCommitInfoNeedsSave(buf);
diff --git a/src/backend/storage/ipc/procarray.c b/src/backend/storage/ipc/procarray.c
index 2473881e8f..65fca7171a 100644
--- a/src/backend/storage/ipc/procarray.c
+++ b/src/backend/storage/ipc/procarray.c
@@ -1000,6 +1000,18 @@ TransactionIdIsActive(TransactionId xid)
  * This is also used to determine where to truncate pg_subtrans.  allDbs
  * must be TRUE for that case, and ignoreVacuum FALSE.
  *
+ * Note: it's possible for the calculated value to move backwards on repeated
+ * calls. The calculated value is conservative, so that anything older is
+ * definitely not considered as running by anyone anymore, but the exact
+ * value calculated depends on a number of things. For example, if allDbs is
+ * TRUE and there are no transactions running in the current database,
+ * GetOldestXmin() returns latestCompletedXid. If a transaction begins after
+ * that, its xmin will include in-progress transactions in other databases
+ * that started earlier, so another call will return an lower value. The
+ * return value is also adjusted with vacuum_defer_cleanup_age, so increasing
+ * that setting on the fly is an easy way to have GetOldestXmin() move
+ * backwards.
+ *
  * Note: we include all currently running xids in the set of considered xids.
  * This ensures that if a just-started xact has not yet set its snapshot,
  * when it does set the snapshot it cannot set xmin less than what we compute.